Error-compensated position determining

ABSTRACT

The present system determines the linear position of a machine tool slide driven by a lead screw. The rotational position of the lead screw is sensed by an analog-to-digital converter which produces a number designating the nominal linear position of the slide corresponding to the sensed rotational position of the lead screw. The system has an error program containing, for each oneinch increment along the lead screw, a digital error signal which represents the mean deviation between the slide&#39;&#39;s actual position and its nominal position for that increment of the slide travel. The proper error signal is selected from this program in response to the inch-designating digits in the output number from the analog-to-digital converter. The selected digital error signal is combined with the latter number, either by addition or subtraction, to produce a corrected number which more accurately designates the actual linear position of the slide, thereby compensating for lead screw error. This corrected number is combined with a zero offset number to provide an offset-corrected number which designates the slide position with respect to a chosen offset zero location along the lead screw. This offsetcorrected number is displayed visually as a decimal number.

United States Patent Corde s, Jr. I

[54] ERROR-COMPENSATED POSITION DETERMINING abandoned.

' [52] US. Cl ..340/347 R, 340/347 P, 235/154, 7 235/l5l.ll,318/632 [51]Int. Cl. ..G08C 9/00 [58] Field of Search-...340/347AD;'235/lS4, 151.11;

[4 1 Dec. 5, 1972 Primary Examiner-Maynard R. Wilbur AssistantExaminer-Charles D. Miller Attorney+Yount, Flynn & Tarolli [5 7]ABSTRACT The present system determines the linear position of a machinetool slide driven by a lead screw. The rotational position of the leadscrew is sensed by an analog-to-digital converter which produces anumber designating the nominal linear position of the slidecorresponding to the sensed rotational position of the lead screw. Thesystem has an error program containing, for each one-inch incrementalong the lead screw, a digital error signal which represents the meandeviation between the slides actual position and its nominal positionfor that increment of the slide travel. The proper error signal isselected from this program in response to the inch-designating digits inthe output number from the analog-to-digital converter. The selecteddigital error signal is combined with the latter number, either byaddition or subtraction, to produce [56] I References Cited a correctednumber which more accurately designates UNITED STATES PATENTS the actuallinear position of the slide, thereby compensating for lead screw error.ThlS corrected number 18 Bralnard ombined a zero offset number toprovide an off 3,492,467 I 1'/1970 Caban et a1. ..235/ 151.11 setconected number Which designates h slide posi 3,491,278 l/ 1970 Stobbe..318/ 162 tion with respem to a chosen offset zero location along3,449,554 6/1969 Kelllng ..235/15l.1l the lead Screw This ff t t dnumber is played visually as a decimal number.

Claims, 2 Drawing Figures DESIGNATING ROTATIONAL 1 POSITION OF LEADscaew L l R B c D c a c o -BINAY -B..D. Numaea /NUMBER f as [24 f2?INARY CODE. ZNCODER oecwsk r80 susrmr susmr CONVERTER C C I CIRCUIT 2a,V b IR U T DISPLAY- B. C. D B.C.D. ERROR I8 86 DECIMAL PROGRAM I5 25 O IINCH z ERO 2 DETECIIONi sgr INCH GATES ERROR-COMPENSATED POSITIONDETERMINING This application is a continuation of application Ser. No.665,337, filed Sept. 5, 1967 now abandoned.

This invention relates to a system for determining the position ofamovable member, particularly a linearlymoving member driven by a rotarydriving member, such as a machine tool slide driven by a lead screw.

The present system is particularly adapted for use in a machine toolhaving a rotary driving member, such as a lead screw, which drivinglyengages a nut on a linearly-moving driven part of the machine tool, suchas a slide or carriage. Various analog-to-digital converters have beenproposed heretofore which sense the rotational or angular position ofthe lead screwor other rotary driving member and produce a numberrepresenting the sensed rotational position. If the screw-threaded drivecoupling between the lead screw and the linearly-moving driven memberwere completely error-free, then this number would also designate thelinear position of the driven member from a predetermined referenceposition. However, in actual practice, a lead screw error is usuallypresent andto offset this error the'present system has novel provisionfor correcting the reading of the linear position of the driven memberin an advantageous manner.

Prior to the present invention it has been proposed to offset the leadscrew error by providing an analog correction signal from a cam whosecurvature represents the errorbetween the rotational position of thelead screw and the linear position of the driven member. This has thedisadvantages of making it necessary to specially machine a cam for eachlead screw to compensate for its error and to provide relatively complexand expensive equipment to apply this analog correction signal to thereadout for the linearly-movable member. Also, progressive wear on thelead screw would require machining a new cam to provide the correcterror compensation.

In its preferred embodiment, the present invention overcomes thesedisadvantages by providing an error signal'program which produces anindividual digital errorsignal for eachincrement of movement of thedriven member, and means for selecting the proper error signal from theprogram to modify the digital signal which designates the actualrotational position of the lead screw and the nominal position of thedriven member, so as to produce a corrected digital signal which moreaccurately designates the actual linear position of the driven member.The use of digital error signals enables the electronic circuitry of thepresent system to be relatively simple, while providing a high degree ofaccuracy.

It is a principal object of this invention to provide a novel andimproved system for determining the position of a movable member inwhich the error between the nominal or apparent position of the movablemember and its actual position is compensated by an error signal whichcorrects a signal designating its nominal or apparent position.

Another object of this invention is to provide a novel andimprovedsystem for determining the position of a linearly-movable memberwhich is driven by a rotary driving member, in which the error betweenthe nominal position of the linearly-movable member, as

designated by a digital number indicating the rotational position of thedriving member, and its actual linear position is corrected by a digitalerror signal selected from an error program which contains an errorsignal for each of the successive increments of the driven memberstravel.

Another object of this invention is to provide such a system in whichthe digital error signals in the error program may be changed readilyand conveniently to reflect changes in the actual error of the drive tothe linearly-movable driven member, such as might be caused by wear on alead screw.

Further objects and advantages of this invention will be apparent fromthe following detailed description of a presently-preferred embodimentwith reference to the accompanying drawing.

In the drawing:

FIG. 1 is a schematic blockdiagram showing the system of the presentinvention; and

FIG. 2 shows a graph in which slide position error is plotted againstthe actual slide position, with the dashed line showing theuncompensated error curve, and the full line curve segments showing theerror curve after being compensated by the system of the presentinvention.

Referring to FIG. 1, the present system is shown in block diagram formin association with a rotary lead screw 10 which is in screw-threadeddriving engagement with a linearly-movable slide 11 of a machine tool,for example. The lead screw 10 is coupled mechanically to the rotatableinput shaft of a binary encoder 12, as indicated schematically by thedashed line 13.

The encoder 12 preferably may be of the type dis-. closed and claimed inthe copending US. Pat. application of Ralph H. Schuman, Ser. No.560,951, filed June 6, 1966 and assigned to the same assignee as thepresent invention. That encoder has a rotatable code wheel 12a which isdriven with the screw 10 and has six encoding sections for providing anumber including a total of six digit places, including four decimalplaces. Each of the six encoding sections in the encoder 12 is read by areader 12b which produces a group of binary outputsigna ls which areapplied to corresponding logic sections in a decoder 14. Each of theselogic sections in the decoder 14 contains logic elements which arearranged in accordance with the proper binary-coded decimal code forthat particular section of the encoder so as to produce output signalsrepresenting the binary digits weighted l, 2, 4 and 8 for each decade ordigit place of the number. The output from the decoder 14 is abinary-coded decimal number which designates the rotational or angularposition of the lead screw 10, but is calibrated in accordance with thecorresponding ap parent or nominal linear position of the slide 11 forthat rotational position of the lead screw (i.e., ignoring the leadscrew error). For example, the least significant digit position of thisnumber may designate the nominal linear position of the slide 11 inten-thousandths of an inch, the next digit position of this numberdesignates the nominal linear position of the slide in thousandths of aninch, and so on. The fifth and sixth digit positions of this numberdesignate the nominal linear position of the slide in inches and tens ofinches, respectively.

The two logic sections of the decoder which respectively provide theinch and tens of inches designations are connected to inch detectioncircuitry 15, which detects each nominal inch position of the slide 11driven by the lead screw. In one practical embodiment, the maximumstraight-line travel of the slide 11 may be 20 inches, for example. Theinch detection circuitry 15, in response to the output signals which itreceives from these two sections of the decoder 14, determines whetherthe rotational movement undergone by the lead screw is such that theslide should be somewhere between its zero and one inch position, orbetween its one inch and two inch positions, or between 2 and 3, etc.

I The output of the inch detection circuitry 15 is connected to inchgate circuitry 16 having a gating section for each of the one-inchincrements into which the slide movement is divided. That is, there is agating section for the nominal positions of the slide from to I, agating section for the nominal positions from 1 to 2, and so on for eachof the successive one-inch increments along the lead screw.

These gating sections are connected individually to corresponding errorprogram signal sources 17, one for each of the one-inch increments alongthe lead screw. Each gating section is normally closed to prevent thecorresponding error program signal from passing to the output line 18,except when that gating section receives a signal from the inchdetection circuitry telling it that the nominal position of the slide 11is within the corresponding l-inch increment along the lead screw 10.

Each error signal source may be provided by an error program cardcarrying a set of eight diodes having different binary-number weightsand capable of producing a binary-coded decimal number output anywherefrom 00 to 99 in the two least significant digit places. In the caseunder discussion, 7 these are the tenthousandths and the thousandths ofan inch digit places.

Each of the error program signal sources 17 provides a correction signalsubstantially equal to the mean deviation of the actual position of theside 11 from its nominal or apparent position, as determined by therotational position of the lead screw 10, for the corresponding one-inchincrement along the lead screw. This is done by providing a calibrationcurve for the lead screw, which may be prepared by measuring the actuallinear travel of the slide 11 with a laser interferometer and comparingit with the nominal slide travel as indicated by the encoder 12.

The dashed-line curve in FIG. 2 shows the error in the nominal slideposition reading plotted against actualslide position from zero to 10inches,'where the lead screw error throughout is such that the encoderreadings are too high-that is, the slide actually moves a slightlyshorter distance along the lead screw for each one-inch increment thanwhat is indicated by the encoder 12. Since the error is in the samedirection for each inch increment, the cumulative error over the fullten inches of slide travel can be quite substantial. The

error in the encoder reading is shown as positive in sign.

In the present system the total error in each one-inch increment of theslide travel is compensated by determining the mean deviation or errorin that particular increment between the nominal slide position and itsactual position. For example, in the dashed-line curve of FIG. 2, in theincrement of slide travel from 0 to 1 inch, the mean deviation issubstantially 0.0002 inch. Therefore, the error program for the 0-1increment is such that it produces an error signal representing 0.0002inch. This error signal input to the corresponding inch gating sectionin the gate circuitry 16 is in binary-coded decimal form.

In the example shown in FIG. 2, the encoder zero is set to match theslide zero position-Le, the encoder reading is correct at the zeroposition of the slide along the lead screw.

At the start of the slide travel over the increment from 0 to l, the 0-linch gating section in the inch gate circuitry 16 will be opened (inresponse to a signal from the inch detection circuitry 15) to pass this0.0002 inch error signal from the 0-1 error signal source via line 18 tothe input of a subtract circuit 19. The subtract circuit 19 is an adderwhich operates on the principle of nines complement arithmetic tosubtract one input signal from another input signal. The constant 0.0002inch error signal is applied continuously to the subtract circuit 19 aslong as the slide 11 is between its nominal 0 and 1 inch positions, asdetected by the inch detection circuitry 15. The complete binary-codeddecimal output signal from the decoder 14, which designates the apparentor nominal position of the slide 11 along the lead screw 10, is appliedcontinuously via line 20 to the subtract circuit 19. The subtractcircuit 19 subtracts the 0-1 error signal (designating the 0.0002 inchmean error for the 0-1 increment) from the output signal of decoder 14(representing the nominal position of the slide) throughout all nominalpositions of the slide from 0 to 1 inch. This has the effect ofdisplacing the error curve for the 0-1 increment of the slide travelfrom the corresponding portion of the dashed-line curve in FIG. 2 downto the full-line curve segment 21, which extends substantially equallyabove and below the zero error line. The mean error value of this curvesegment 21 is substantially zero.

Similarly, when the slide 11 passes the nominal I inch position alongthe lead screw 10, the 0-1 inch gating section in the inch gatingsection circuitry 16 will be closed, and the 1-2 inch gate will beopened (in response to a signal from the inch detection circuitry 15) topass the l-2 increment error signal from the error program. This l-2increment error signal is determined by the mean value of the error ofthe dashed-line curve of FIG. 2 between the l-inch and 2-inch slidetravel positions, as already stated. In the specific example shown inFIG. 2, this mean error value between positions 1 and 2 is substantially0.0004 inch.

This constant 0.0004 inch error signal is passed from the l-2 errorsignal source through the respective gating section to the output line18 leading to the subtract circuit 19 until the slide reaches thenominal 2-inch position along the lead screw, as detected by the inchdetection circuitry l5.-At the same time, the complete binary-codeddecimal output signal from the decoder 14 is applied via line 20 to thesubtract circuit 19, which subtracts the l-2 error signal (designatingthe mean error value of 0.0004 inch) from the decoder output signal.This has the effect of displacing the error curve for the l-2 inchincrement of the slide travel from the corresponding portion of thedashed-line curve in FIG. 2 down to the full-line curve segment 22. Themean value of this displaced curve segment 22 is substantially zero.

Similar corrective actions take place for the slide travel through eachof the successive 1-inch increments 2-3, 3-4, 4-5, etc. In eachinstance, throughout the slide travel over each respective 1-inchincrement, the corresponding error signal is applied continuously to thesubtract circuit 19 so that the mean error (between the nominal slideposition, as sensed by the encoder l2, and the actual slide position)issubstantially zero over this increment of the slide travel.

Thus, for each l-inch increment of the slide travel the error in anyinstantaneous position of the slide is never more than about one-halfthetotal error accumu lated during this one-inch increment alone. Also,the errors for successive one-inch increments of the slide travel arenot accumulated because an individual correction is made for the erroroccurring in each one-inch increment in succession.

The output signal from the subtract circuit 19 is a binary-coded decimalnumber which is applied via line 23 to the input of a second subtractcircuit 24. A zero offset number in binary-coded decimal form also isapplied from a signal source 25 via line 26 to the input of the secondsubtract circuit 24. The magnitude of this zero offset numbercorresponds to the distance along the lead screw between a chosen zerooffset position and the slide zero position at which the reading of theencoder12 is zero. This zero offset number is subtracted from thecorrected number output from circuit 19 to designate the position of theslide 11 with respect to the chosen offset zero position along the leadscrew.

The offset-corrected output signal from the secondsubtract circuit is abinary-coded decimal number which is converted to decimal form in a codeconverter 27. This decimal number then is displayed in a visual displaydevice 28. i

If the lead screw error is such as to produce a slide lead throughoutthe slide travel (i.e., the encoder readings will be too low by theamount of the accumulated slide lead error), the encoder 12 is set toexactly match the actual slide position when the latter is in itsmaximum range position (e.g., the 20-inch position when the maximumslide travel is 20 inches). This enables the operations in the subtractcircuits 19 and 24 to be subtractions only, which simplifies thesecircuits. i

If the lead screw error produces a slide lead for part of its length anda slide lag for theremainder, the encoder 1-2 would be set to match theactual slide position at the position of maximum error or excursion ofthe slide along the lead screw. This enables the circuits l9 and 24 tooperate by subtracting the error number from the encoder number .at anyincremental position of the slide along the lead screw.

Alternatively, by the use of a more complex add/subtract and signdecision circuit in place of each of the subtract circuits l9 and 24,the modification of the encoder number by the selected number from theerror program might be either an addition or a subtraction, dependingupon whether the mean error for that particularincrement of the slidetravel is a slide lead or a slide lag error. This would require theadd/subtract circuit to have provision for determining whether theoperation should be addition or subtraction.

From the foregoing description it will be evident that the illustratedsystem involves only the modification of one digital number by anotherdigital number, which can be carried out accurately by relatively simplecircuitry. Any change in the lead screw error in any increment along thelength of the lead screw, such as might occur due to wear on the leadscrew over a period of use, can be corrected by replacing the errorprogram card for that increment so as to provide the proper errorsignals for the worn lead screw. Such replacement can be done morereadily and much less expensively than the replacement of a cam servingas the error signal source.

While a presently-preferred embodiment of this invention has beendescribed in detail and illustrated schematically in the accompanyingdrawing, it is to be understood that the present system is susceptibleof other embodiments differing from the particular arrangement describedwithout departing from the spirit and scope of this invention. Forexample, the lead screw increments into which the error program isdivided may be larger or smaller than the one-inch increments described.Also, the drive coupling might be a gear and rack, instead of a leadscrew and nut arrangement. Also, the present invention might be embodiedin a system in which the nominal position and the error signal areprovided by analog signals, with the appropriate error signal beingselected in response to the detection of the nominal position of thedriven member.

Having described my invention, the following is claimed:

1. An apparatus for determining the position of a movable member along apredetermined path comprising drive means for driving the movable memberalong the predetermined path, indicating means for rendering signalsindicating nominal positions of said movable member as it is moved alongthe predetermined path by said drive means, said nominal positionsindicated by said indicating means differing from actual position of themovable member as it moves along the predetermined path by amounts whichvarywith movement of the movable member along the predetermined path,correction signal means operating in response to the signalsrepresenting nominal positions of said movable member for providingcorrection signals which vary in magnitude with changes in thenominalposition of the movable member as the movable member moves along thepredetermined path, said correction signal means being operable to varythe magnitude of said correction signals as a function of variations inthe difference between the actual positions to which said movable memberis driven by said drive means and the nominal positions of said movablemember represented by the signals rendered by said indicating means assaid movable member moves along said predetermined path, and means forcombining said correction signals and said signals rendered by saidindicating means to produce third electrical signals which are moreaccurately indicative of the positions of said movable member as saidmovable member moves along the predetermined path than are saidelectrical signals rendered by said indicating means.

2. Apparatus as set forth in claim 1 further including means forproviding visual display of a decimal number corresponding to said thirdelectrical signals.

3. Apparatus as set forth in claim 2 wherein said decimal numberdesignates the position of said movable member from an offset zeroposition.

4. An'apparatu's as set forth in claim 1 wherein said drive means isoperable to move said movable member sequentially through a plurality ofcontiguous zones located along said predetermined path, and saidcorrection signal means includes a plurality of information storagemeans each of which is associated with one of said zones and has storedinformation which corresponds to the difference between the nominalposition indicated by said indicating means and the actual position ofthe movable member when the movable member is located in the zoneassociated with said information storage means.

5. An apparatus as set forth in claim 4 wherein the stored informationin each of said information storage means corresponds to the meandeviation of the difference between the nominal positions and actualpositions of said movable member as it moves through an associated oneof said zones.

6. An apparatus as set forth in claim 5 wherein said drive meansincludes a lead screw. 7

7. An apparatus for determining the position of a movable member along apredetermined path comprising indicating means for rendering anindication of the position of said movable member, said indicating meansincluding positionable means having positions which correspond topositions of the movable member, drive means for driving the movablemember and said positionable means, said positionable means being drivenby said drive means to positions which differ from the positionscorresponding to the positions of the movable member along thepredetermined path, reader means cooperating with said positionablemeans to sense the positions thereof and to render first electricalsignals indicative of the positions of said movable member asrepresented by the positions of said positionable means, correctionsignal means operating in dependency on the position of saidpositionablemeans for providing second electrical signals which vary in magnitude asa function of variations in the difference between the positions towhich said positionable means is driven by said drive means and thepositions of said positionable means which correspond to the positionsof said movable member as said movable member is moved along saidpredetermined path, and means for combining said first and secondelectrical signals to produce third electrical signals indicative of thepositions of said movable member and which are more accurate than saidfirst electrical signals.

8. An apparatus as defined in claim 7 wherein said drive means comprisesa lead screw which rotates to impart movement to said movable member.

9. An apparatus as defined in claim 7 wherein said movable member issequentially movable through a plurality of contiguous zones located onsaid predetermined path, and said correction signal means for producinga plurality of second signals includes a plurality of informationstorage means each of which is associated with one of said zones and hasstored information which corresponds to an error associated with saidfirst electrical signal roduced when said movable member is locate in te zone associated with said information carrying means.

10. An apparatus as defined in claim 9 wherein said positionable meanscomprises an encoding means with said one of said information storagemeans.

12. An apparatus as defined in claim 11 wherein said drive meanscomprises a lead screw which rotates to impart movement to the movablemember.

13. A method of determining the position of a movable member which movesalong a path, said method including the steps of measuring actualpositions of the movable member as the member moves along the path,rendering a plurality of indications corresponding to the measuredpositions of the movable member as the member moves along the path,comparing the indicated positions of the movable member with thecorresponding measured positions of the movable member to derive aplurality of error factors having magnitudes which vary as a function ofvariations in the differences between the measured positions of themovable member and the positions represented by the correspondingindications, storing the error factors in an error factor storage means,moving said movable member along the path, rendering indicationscorresponding to the position of the movable member, activating theerror factor storage means to provide error signals which vary inmagnitude in accordance with variations in the position of the movablemember and the associated error factors as the member moves along thepath, and combining the error signals and the indications of thepositions of the movable member to derive position signals indicative ofthe positions of the movable member and which are more accurate than theindications as the member moves along the path.

14. A method of determining the position of a movable member as isdefine in claim 13 wherein the step of comparing the indicated positionsof the movable member with the corresponding measured position of themovable member includes the step of determining the mean deviation ofthe error associated with the indications when the member is in each ofa plurality of zones along the predetermined path and wherein said stepof activating the error factor storage means comprises the step ofinitiating an error signal which is associated with the zone in whichthe member is located and which is equal to the mean deviation of theerror for the indications of that particular zone.

1. An apparatus for determining the position of a movable member along apredetermined path comprising drive means for driving the movable memberalong the predetermined path, indicating means for rendering signalsindicating nominal positions of said movable member as it is moved alongthe predetermined path by said drive means, said nominal positionsindicated by said indicating means differing from actual position of themovable member as it moves along the predetermined path by amounts whichvary with movement of the movable member along the predetermined path,correction signal means operating in response to the signalsrepresenting nominal positions of said movable member for providingcorrection signals which vary in magnitude with changes in the nominalposition of the movable member as the movable member moves along thepredetermined path, said correction signal means being operable to varythe magnitude of said correction signals as a function of variations inthe difference between the actual positions to which said movable memberis driven by said drive means and the nominal positions of said movablemember represented by the signals rendered by said indicating means assaid movable member moves along said predetermined path, and means forcombining said correction signals and said signals rendered by saidindicating means to produce third electrical signals which are moreaccurately indicative of the positions of said movable member as saidmovable member moves along the predetermined path than are saidelectrical signals rendered by said indicating means.
 2. Apparatus asset forth in claim 1 further including means for providing visualdisplay of a decimal number corresponding to said third electricalsignals.
 3. Apparatus as set forth in claim 2 wherein said decimalnumber designates the position of said movable member from an offsetzero position.
 4. An apparatus as set forth in claim 1 wherein saiddrive means is operable to move said movable member sequentially througha plurality of contiguous zones located along said predetermined path,and said correction signal means includes a plurality of informationstorage means each of which is associated with one of said zones and hasstored information which corresponds to the difference between thenominal position indicated by said indicating means and the actualposition of the movable member when the movable member is located in thezone associated with said information storage means.
 5. An apparatus asset forth in claim 4 wherein the stored information in each of saidinformation storage means corresponds to the mean deviation of thedifference between the nominal positions and actual positions of saidmovable member as it moves through an associated one of said zones. 6.An apparatus as set forth in claim 5 wherein said drive means includes alead screw.
 7. An apparatus for determining the position of a movablemember along a predetermined path comprising indicating means forrendering an indication of the position of said movable member, saidindicating means including positionable means having positions whichcorrespond to positions of the movable member, drive means for drivingthe movable member and said positionable means, said positionable meansbeing driven by said drive means to positions which differ from thepositions corresponding to the positions of the movable member along thepredetermined path, reader means cooperating with said positionablemeans to sense the positions thereof and to render first electricalsignals indicative of the positions of said movable member asrepresented by the positions of said positionable means, correctionsignal means operating in dependency on the position of saidpositionable means for providing second electrical signals which vary inmagnitude as a function of variations in the difference between thepositions to which said positionable means is driven by said drive meansand the positions of said positionable means which correspond to thepositions of said movable member as said movable member is moved alongsaid predetermined path, and means for combining said first and secondelectrical signals to produce third electrical signals indicative of thepositions of said movable member and which are more accurate than saidfirst electrical signals.
 8. An apparatus as defined in claim 7 whereinsaid drive means comprises a lead screw which rotates to impart movementto said movable member.
 9. An apparatus as defined in claim 7 whereinsaid movable member is sequentially movable through a plurality ofcontiguous zones located on said predetermined path, and said correctionsignal means for producing a plurality of second signals includes aplurality of information storage means each of which is associated withone of said zones and has stored information which corresponds to anerror associated with said first electrical signal produced when saidmovable member is located in the zone associated with said informationcarrying means.
 10. An apparatus as defined in claim 9 wherein saidpositionable means comprises an encoding means which is driven insynchronism with said movable member and said first electrical signal isderived from position codes therein.
 11. An apparatus as defined inclaim 9 wherein the information stored by each one of said informationstorage means corresponds to the mean of the difference between thepositions to which said positionable means is driven by said drive meansand the positions of said positionable means which correspond to thepositions of said movable member as the movable member moves through thezone which is associated with said one of said information storagemeans.
 12. An apparatus as defined in claim 11 wherein said drive meanscomprises a lead screw which rotates to impart movement to the movablemember.
 13. A method of determining the position of a movable memberwhich moves along a path, said method including the steps of measuringactual positions of the movable member as the member moves along thepath, rendering a plurality of indications corresponding to the measuredpositions of the movable member as the member moves along the path,comparing the indicated positions of the movable member with thecorresponding measured positions of the movable member to derive aplurality of error factors having magnitudes which vary as a function ofvariations in the differences between the measured positions of themovable member and the positions represented by the correspondingindications, storing the error factors in an error factor storage means,moving said movable member along the path, rendering indicationscorresponding to the position of the movable member, activating theerror factor storage means to provide error signals which vary inmagnitude in accordance with variations in the position of the movablemember and the associated error factors as the member moves along thepath, and combining the error signals and the indications of thepositions of the movable member to derive position signals indicative ofthe positions of the movable member and which are more accurate than theindications as the member moves along the path.
 14. A method ofdetermining the position of a movable member as is define in claim 13wherein the step of comparing the indicated positions of the movablemember with the corresponding measured position of the movable membeRincludes the step of determining the mean deviation of the errorassociated with the indications when the member is in each of aplurality of zones along the predetermined path and wherein said step ofactivating the error factor storage means comprises the step ofinitiating an error signal which is associated with the zone in whichthe member is located and which is equal to the mean deviation of theerror for the indications of that particular zone.